Question 7: Waves

Question

The driver of a car travelling with speed $$30 \mathrm{~ms}^{-1}$$ towards a hill sounds a horn of frequency $$600 \mathrm{~Hz}$$. If the velocity of sound in air is $$330 \mathrm{~ms}^{-1}$$, the frequency of reflected sound as heard by driver is :

Accepted Answer

To find the frequency of the reflected sound as heard by the driver, we can break the problem into two steps:
Calculate the Frequency Heard by the Hill:
When the car is moving towards the hill, the frequency of the sound heard by the hill ($f'$) changes due to the Doppler effect. The formula for this scenario (source moving towards a stationary observer) is:
$$ f' = f \left( \frac{v + v_0}{v} ight), $$
where:
$ f = 600 \, 	ext{Hz} $ is the original frequency of the horn.
$ v = 330 \, 	ext{m/s} $ is the speed of sound in air.
$ v_0 = 30 \, 	ext{m/s} $ is the speed of the car (source).
Substituting the values, we have:
$$ f' = 600 \left( \frac{330 + 30}{330} ight) = 600 \left( \frac{360}{330} ight) = 600 	imes \frac{12}{11} = 654.54 \, 	ext{Hz}. $$
Calculate the Frequency of the Reflected Sound Heard by the Driver:
The reflected sound now acts as a new source of frequency $ f' $ as calculated above. Since the driver is moving towards this new source (the hill), we apply the Doppler effect again:
$$ f'' = f' \left( \frac{v}{v - v_0} ight). $$
Substituting the values:
$$ f'' = 654.54 \left( \frac{330}{330 - 30} ight) = 654.54 \left( \frac{330}{300} ight) = 654.54 	imes \frac{11}{10} = 720 \, 	ext{Hz}. $$
Thus, the frequency of the reflected sound as heard by the driver is:
Option C: $720 \, 	ext{Hz}$.

Answer

$$550 \mathrm{~Hz}$$

Answer

$$555.5 \mathrm{~Hz}$$

Answer

$$720 \mathrm{~Hz}$$

Answer

$$500 \mathrm{~Hz}$$

Waves

The driver of a car travelling with speed $30 \mathrm{~ms}^{-1} towards a hill sounds a horn of frequency 600 \mathrm{~Hz}. If the velocity of sound in air is 330 \mathrm{~ms}^{-1}$, the frequency of reflected sound as heard by driver is :

Choose the correct answer: